Theorems · Theorem · general topology
ContinuousMap.isUnit_iff_forall_ne_zero
∀ {X : Type u_1} {R : Type u_3} [inst : TopologicalSpace X] [inst_1 : NormedDivisionRing R] [CompleteSpace R]
(f : C(X, R)), IsUnit f ↔ ∀ (x : X), f x ≠ 0- Defined in
- Mathlib.Topology.ContinuousMap.Units
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- CompleteSpacestatement and proof · cited by 2,532
- ContinuousMapstatement and proof · cited by 2,491
- IsUnitstatement · cited by 1,602
- NormedDivisionRingstatement and proof · cited by 360
- ContinuousMap.isUnit_iff_forall_isUnitproof · cited by 1
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